t81_558_class_06_2_cnn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/jeffheaton/t81_558_deep_learning/blob/master/t81_558_class_06_2_cnn.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YDTXd8-Lmp8Q"
   },
   "source": [
    "# T81-558: Applications of Deep Neural Networks\n",
    "**Module 6: Convolutional Neural Networks (CNN) for Computer Vision**\n",
    "* Instructor: [Jeff Heaton](https://sites.wustl.edu/jeffheaton/), McKelvey School of Engineering, [Washington University in St. Louis](https://engineering.wustl.edu/Programs/Pages/default.aspx)\n",
    "* For more information visit the [class website](https://sites.wustl.edu/jeffheaton/t81-558/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ncNrAEpzmp8S"
   },
   "source": [
    "# Module 6 Material\n",
    "\n",
    "* Part 6.1: Image Processing in Python [[Video]](https://www.youtube.com/watch?v=4Bh3gqHkIgc&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_06_1_python_images.ipynb)\n",
    "* **Part 6.2: Keras Neural Networks for Digits and Fashion MNIST** [[Video]](https://www.youtube.com/watch?v=-SA8BmGvWYE&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_06_2_cnn.ipynb)\n",
    "* Part 6.3: Implementing a ResNet in Keras [[Video]](https://www.youtube.com/watch?v=qMFKsMeE6fM&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_06_3_resnet.ipynb)\n",
    "* Part 6.4: Using Your Own Images with Keras [[Video]](https://www.youtube.com/watch?v=VcFja1fUNSk&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_06_4_keras_images.ipynb)\n",
    "* Part 6.5: Recognizing Multiple Images with YOLO Darknet [[Video]](https://www.youtube.com/watch?v=oQcAKvBFli8&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_06_5_yolo.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Google CoLab Instructions\n",
    "\n",
    "The following code ensures that Google CoLab is running the correct version of TensorFlow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fU9UhAxTmp8S"
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    %tensorflow_version 2.x\n",
    "    COLAB = True\n",
    "    print(\"Note: using Google CoLab\")\n",
    "except:\n",
    "    print(\"Note: not using Google CoLab\")\n",
    "    COLAB = False\n",
    "\n",
    "# Nicely formatted time string\n",
    "def hms_string(sec_elapsed):\n",
    "    h = int(sec_elapsed / (60 * 60))\n",
    "    m = int((sec_elapsed % (60 * 60)) / 60)\n",
    "    s = sec_elapsed % 60\n",
    "    return f\"{h}:{m:>02}:{s:>05.2f}\""
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Jf_otSJdmp8k"
   },
   "source": [
    "# Part 6.2: Keras Neural Networks for Digits and Fashion MNIST\n",
    "\n",
    "# Computer Vision\n",
    "\n",
    "This class will focus on computer vision.  There are some important differences and similarities with previous neural networks.\n",
    "\n",
    "* We will usually use classification, though regression is still an option.\n",
    "* The input to the neural network is now 3D (height, width, color)\n",
    "* Data are not transformed, no z-scores or dummy variables.\n",
    "* Processing time is much longer.\n",
    "* We now have different layer times: dense layers (just like before), convolution layers and max pooling layers.\n",
    "* Data will no longer arrive as CSV files. TensorFlow provides some utilities for going directly from image to the input for a neural network.\n",
    "\n",
    "\n",
    "# Computer Vision Data Sets\n",
    "\n",
    "There are many data sets for computer vision.  Two of the most popular are the MNIST digits data set and the CIFAR image data sets.\n",
    "\n",
    "### MNIST Digits Data Set\n",
    "\n",
    "The [MNIST Digits Data Set](http://yann.lecun.com/exdb/mnist/) is very popular in the neural network research community.  A sample of it can be seen here:\n",
    "\n",
    "![MNIST Data Set](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_8_mnist.png \"MNIST Data Set\")\n",
    "\n",
    "This data set was generated from scanned forms.\n",
    "\n",
    "![Exam](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_8_exam.png \"Exam\")\n",
    "\n",
    "### MNIST Fashion Data Set\n",
    "\n",
    "[Fashion-MNIST](https://www.kaggle.com/zalando-research/fashionmnist) is a dataset of [Zalando](https://jobs.zalando.com/tech/)'s article images—consisting of a training set of 60,000 examples and a test set of 10,000 examples. Each example is a 28x28 grayscale image, associated with a label from 10 classes. Fashion-MNIST is intended to serve as a direct **drop-in replacement** for the original [MNIST dataset](http://yann.lecun.com/exdb/mnist/) for benchmarking machine learning algorithms. It shares the same image size and structure of training and testing splits.\n",
    "\n",
    "![mnist-fashion](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/mnist-fashion.png \"mnist-fashion\")\n",
    "\n",
    "### CIFAR Data Set\n",
    "\n",
    "The [CIFAR-10 and CIFAR-100](https://www.cs.toronto.edu/~kriz/cifar.html) datasets are also frequently used by the neural network research community.\n",
    "\n",
    "![cifar-10](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_8_cifar.png \"cifar-10\")\n",
    "\n",
    "The CIFAR-10 data set contains low-rez images that are divided into 10 classes.  The CIFAR-100 data set contains 100 classes in a hierarchy. \n",
    "\n",
    "# Other Resources\n",
    "\n",
    "* [Imagenet:Large Scale Visual Recognition Challenge 2014](http://image-net.org/challenges/LSVRC/2014/index)\n",
    "* [Andrej Karpathy](http://cs.stanford.edu/people/karpathy/) - PhD student/instructor at Stanford.\n",
    "    * [CS231n Convolutional Neural Networks for Visual Recognition](http://cs231n.stanford.edu/) - Stanford course on computer vision/CNN's.\n",
    "        * [CS231n - GitHub](http://cs231n.github.io/)\n",
    "    * [ConvNetJS](http://cs.stanford.edu/people/karpathy/convnetjs/) - JavaScript library for deep learning.\n",
    " \n",
    "\n",
    "# Convolutional Neural Networks (CNNs)\n",
    "\n",
    "The convolutional neural network (CNN) is a neural network technology that has profoundly impacted the area of computer vision (CV). Fukushima  (1980) introduced the original concept of a convolutional neural network, and   LeCun, Bottou, Bengio & Haffner (1998) greatly improved this work. From this research, Yan LeCun introduced the famous LeNet-5 neural network architecture.  This chapter follows the LeNet-5 style of convolutional neural network.  \n",
    "Although computer vision primarily uses CNNs, this technology has some application outside of the field. You need to realize that if you want to utilize CNNs on non-visual data, you must find a way to encode your data so that it can mimic the properties of visual data.  \n",
    "\n",
    "CNNs are somewhat similar to the self-organizing map (SOM) architecture that we examined in Chapter 2, “Self-Organizing Maps.”  The order of the vector elements is crucial to the training. In contrast, most neural networks that are not CNNs or SOMs treat their input data as a long vector of values, and the order that you arrange the incoming features in this vector is irrelevant. For these types of neural networks, you cannot change the order after you have trained the network. In other words, CNNs and SOMs do not follow the standard treatment of input vectors. \n",
    "The SOM network arranged the inputs into a grid.  This arrangement worked well with images because the pixels in closer proximity to each other are important to each other.  Obviously, the order of pixels in an image is significant.  The human body is a relevant example of this type of order. For the design of the face, we are accustomed to eyes being near to each other.  In the same way, neural network types like SOMs adhere to an order of pixels. Consequently, they have many applications to computer vision. \n",
    "\n",
    "Although SOMs and CNNs are similar in the way that they map their input into 2D grids or even higher-dimension objects such as 3D boxes, CNNs take image recognition to higher level of capability.  This advance in CNNs is due to years of research on biological eyes. In other words, CNNs utilize overlapping fields of input to simulate features of biological eyes. Until this breakthrough, AI had been unable to reproduce the capabilities of biological vision.\n",
    "Scale, rotation, and noise have presented challenges in the past for AI computer vision research.  You can observe the complexity of biological eyes in the example that follows. A friend raises a sheet of paper with a large number written on it.  As your friend moves nearer to you, the number is still identifiable. In the same way, you can still identify the number when your friend rotates the paper.  Lastly, your friend creates noise by drawing lines on top of the page, but you can still identify the number. As you can see, these examples demonstrate the high function of the biological eye and allow you to understand better the research breakthrough of CNNs. That is, this neural network has the ability to process scale, rotation, and noise in the field of computer vision.\n",
    "\n",
    "**A LeNET-5 Network (LeCun, 1998)**\n",
    "![LENET5](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_8_lenet5.png \"LENET5\")\n",
    "\n",
    "So far we have only seen one layer type (dense layers).  By the end of this course we will have seen:\n",
    "\n",
    "* **Dense Layers** - Fully connected layers.  (introduced previously)\n",
    "* **Convolution Layers** - Used to scan across images. (introduced this class)\n",
    "* **Max Pooling Layers** - Used to downsample images. (introduced this class)\n",
    "* **Dropout Layer** - Used to add regularization. (introduced next class)\n",
    "\n",
    "## Convolution Layers\n",
    "\n",
    "The first layer that we will examine is the convolutional layer. We will begin by looking at the hyper-parameters that you must specify for a convolutional layer in most neural network frameworks that support the CNN:\n",
    "\n",
    "* Number of filters\n",
    "* Filter Size\n",
    "* Stride\n",
    "* Padding\n",
    "* Activation Function/Non-Linearity\n",
    "\n",
    "The primary purpose for a convolutional layer is to detect features such as edges, lines, blobs of color, and other visual elements. The filters can detect these features. The more filters that we give to a convolutional layer, the more features it can detect.\n",
    "\n",
    "A filter is a square-shaped object that scans over the image. A grid can represent the individual pixels of a grid. You can think of the convolutional layer as a smaller grid that sweeps left to right over each row of the image. There is also a hyper parameter that specifies both the width and height of the square-shaped filter. Figure 10.1 shows this configuration in which you see the six convolutional filters sweeping over the image grid:\n",
    "\n",
    "A convolutional layer has weights between it and the previous layer or image grid. Each pixel on each convolutional layer is a weight. Therefore, the number of weights between a convolutional layer and its predecessor layer or image field is the following:\n",
    "\n",
    "```\n",
    "[FilterSize] * [FilterSize] * [# of Filters]\n",
    "```\n",
    "\n",
    "For example, if the filter size were 5 (5x5) for 10 filters, there would be 250 weights.\n",
    "\n",
    "You need to understand how the convolutional filters sweep across the previous layer’s output or image grid. Figure 10.2 illustrates the sweep:\n",
    "\n",
    "![CNN](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_8_cnn_grid.png \"CNN\")\n",
    "\n",
    "The above figure shows a convolutional filter with a size of 4 and a padding size of 1. The padding size is responsible for the boarder of zeros in the area that the filter sweeps. Even though the image is actually 8x7, the extra padding provides a virtual image size of 9x8 for the filter to sweep across. The stride specifies the number of positions at which the convolutional filters will stop. The convolutional filters move to the right, advancing by the number of cells specified in the stride. Once the far right is reached, the convolutional filter moves back to the far left, then it moves down by the stride amount and\n",
    "continues to the right again.\n",
    "\n",
    "Some constraints exist in relation to the size of the stride. Obviously, the stride cannot be 0. The convolutional filter would never move if the stride were set to 0. Furthermore, neither the stride, nor the convolutional filter size can be larger than the previous grid. There are additional constraints on the stride (s), padding (p) and the filter width (f) for an image of width (w). Specifically, the convolutional filter must be able to start at the far left or top boarder, move a certain number of strides, and land on the far right or bottom boarder. The following equation shows the number of steps a convolutional operator\n",
    "must take to cross the image:\n",
    "\n",
    "$ steps = \\frac{w - f + 2p}{s+1} $\n",
    "\n",
    "The number of steps must be an integer. In other words, it cannot have decimal places. The purpose of the padding (p) is to be adjusted to make this equation become an integer value.\n",
    "\n",
    "## Max Pooling Layers\n",
    "\n",
    "Max-pool layers downsample a 3D box to a new one with smaller dimensions. Typically, you can always place a max-pool layer immediately following convolutional layer. The LENET shows the max-pool layer immediately after layers C1 and C3. These max-pool layers progressively decrease the size of the dimensions of the 3D boxes passing through them. This technique can avoid overfitting (Krizhevsky, Sutskever & Hinton, 2012).\n",
    "\n",
    "A pooling layer has the following hyper-parameters:\n",
    "\n",
    "* Spatial Extent (f )\n",
    "* Stride (s)\n",
    "\n",
    "Unlike convolutional layers, max-pool layers do not use padding. Additionally, max-pool layers have no weights, so training does not affect them. These layers simply downsample their 3D box input. The 3D box output by a max-pool layer will have a width equal to this equation:\n",
    "\n",
    "$ w_2 = \\frac{w_1 - f}{s + 1} $\n",
    "\n",
    "The height of the 3D box produced by the max-pool layer is calculated similarly with this equation:\n",
    "\n",
    "$ h_2 = \\frac{h_1 - f}{s + 1} $\n",
    "\n",
    "The depth of the 3D box produced by the max-pool layer is equal to the depth the 3D box received as input. The most common setting for the hyper-parameters of a max-pool layer are f =2 and s=2. The spatial extent (f) specifies that boxes of 2x2 will be scaled down to single pixels. Of these four pixels, the pixel with the maximum value will represent the 2x2 pixel in the new grid. Because squares of size 4 are replaced with size 1, 75% of the pixel information is lost. The following figure shows this transformation as a 6x6 grid becomes a 3x3:\n",
    "\n",
    "![MaxPool](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_8_conv_maxpool.png \"MaxPool\")\n",
    "\n",
    "Of course, the above diagram shows each pixel as a single number. A grayscale image would have this characteristic. For an RGB image, we usually take the average of the three numbers to determine which pixel has the maximum value.\n",
    "\n",
    "[More information on CNN's](http://cs231n.github.io/convolutional-networks/)\n",
    "\n",
    "# TensorFlow with CNNs\n",
    "\n",
    "The following sections describe how to use TensorFlow/Keras with CNNs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "E0QVQe3Rmp8k"
   },
   "source": [
    "### Access to Data Sets - DIGITS\n",
    "\n",
    "Keras provides built in access classes for MNIST.  It is important to note that MNIST data arrives already separated into two sets:\n",
    "\n",
    "* **train** - Neural network will be trained with this.\n",
    "* **test** - Used for validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 136
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 30814,
     "status": "ok",
     "timestamp": 1558731578524,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "9A5mOErFmp8l",
    "outputId": "586de8dd-2d14-4be7-bb55-e4e868ecf524"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of x_train: (60000, 28, 28)\n",
      "Shape of y_train: (60000,)\n",
      "\n",
      "Shape of x_test: (10000, 28, 28)\n",
      "Shape of y_test: (10000,)\n"
     ]
    }
   ],
   "source": [
    "import tensorflow.keras\n",
    "from tensorflow.keras.callbacks import EarlyStopping\n",
    "from tensorflow.keras.layers import Dense, Dropout\n",
    "from tensorflow.keras import regularizers\n",
    "from tensorflow.keras.datasets import mnist\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "print(\"Shape of x_train: {}\".format(x_train.shape))\n",
    "print(\"Shape of y_train: {}\".format(y_train.shape))\n",
    "print()\n",
    "print(\"Shape of x_test: {}\".format(x_test.shape))\n",
    "print(\"Shape of y_test: {}\".format(y_test.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4aQApI1jmp8o"
   },
   "source": [
    "### Display the Digits \n",
    "\n",
    "The following code shows what the MNIST files contain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 968
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 30815,
     "status": "ok",
     "timestamp": 1558731578525,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "Abe2m8u_mp8p",
    "outputId": "f7923427-f1c5-49fd-b196-33786c5c1834"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape for dataset: (60000, 28, 28)\n",
      "Labels: [5 0 4 ... 5 6 8]\n",
      "Shape for single: (28, 28)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>18</th>\n",
       "      <th>19</th>\n",
       "      <th>20</th>\n",
       "      <th>21</th>\n",
       "      <th>22</th>\n",
       "      <th>23</th>\n",
       "      <th>24</th>\n",
       "      <th>25</th>\n",
       "      <th>26</th>\n",
       "      <th>27</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>175</td>\n",
       "      <td>26</td>\n",
       "      <td>166</td>\n",
       "      <td>255</td>\n",
       "      <td>247</td>\n",
       "      <td>127</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>36</td>\n",
       "      <td>...</td>\n",
       "      <td>225</td>\n",
       "      <td>172</td>\n",
       "      <td>253</td>\n",
       "      <td>242</td>\n",
       "      <td>195</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>49</td>\n",
       "      <td>238</td>\n",
       "      <td>253</td>\n",
       "      <td>...</td>\n",
       "      <td>93</td>\n",
       "      <td>82</td>\n",
       "      <td>82</td>\n",
       "      <td>56</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>219</td>\n",
       "      <td>253</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>156</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>150</td>\n",
       "      <td>27</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>253</td>\n",
       "      <td>187</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>253</td>\n",
       "      <td>249</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>253</td>\n",
       "      <td>207</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>250</td>\n",
       "      <td>182</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>78</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23</td>\n",
       "      <td>66</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>171</td>\n",
       "      <td>219</td>\n",
       "      <td>253</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>55</td>\n",
       "      <td>172</td>\n",
       "      <td>226</td>\n",
       "      <td>253</td>\n",
       "      <td>253</td>\n",
       "      <td>253</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>136</td>\n",
       "      <td>253</td>\n",
       "      <td>253</td>\n",
       "      <td>253</td>\n",
       "      <td>212</td>\n",
       "      <td>135</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>28 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1   2   3    4    5    6    7    8    9   ...   18   19   20   21  \\\n",
       "0    0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "1    0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "2    0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "3    0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "4    0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "5    0   0   0   0    0    0    0    0    0    0  ...  175   26  166  255   \n",
       "6    0   0   0   0    0    0    0    0   30   36  ...  225  172  253  242   \n",
       "7    0   0   0   0    0    0    0   49  238  253  ...   93   82   82   56   \n",
       "8    0   0   0   0    0    0    0   18  219  253  ...    0    0    0    0   \n",
       "9    0   0   0   0    0    0    0    0   80  156  ...    0    0    0    0   \n",
       "10   0   0   0   0    0    0    0    0    0   14  ...    0    0    0    0   \n",
       "11   0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "12   0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "13   0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "14   0   0   0   0    0    0    0    0    0    0  ...   25    0    0    0   \n",
       "15   0   0   0   0    0    0    0    0    0    0  ...  150   27    0    0   \n",
       "16   0   0   0   0    0    0    0    0    0    0  ...  253  187    0    0   \n",
       "17   0   0   0   0    0    0    0    0    0    0  ...  253  249   64    0   \n",
       "18   0   0   0   0    0    0    0    0    0    0  ...  253  207    2    0   \n",
       "19   0   0   0   0    0    0    0    0    0    0  ...  250  182    0    0   \n",
       "20   0   0   0   0    0    0    0    0    0    0  ...   78    0    0    0   \n",
       "21   0   0   0   0    0    0    0    0   23   66  ...    0    0    0    0   \n",
       "22   0   0   0   0    0    0   18  171  219  253  ...    0    0    0    0   \n",
       "23   0   0   0   0   55  172  226  253  253  253  ...    0    0    0    0   \n",
       "24   0   0   0   0  136  253  253  253  212  135  ...    0    0    0    0   \n",
       "25   0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "26   0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "27   0   0   0   0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "\n",
       "     22   23  24  25  26  27  \n",
       "0     0    0   0   0   0   0  \n",
       "1     0    0   0   0   0   0  \n",
       "2     0    0   0   0   0   0  \n",
       "3     0    0   0   0   0   0  \n",
       "4     0    0   0   0   0   0  \n",
       "5   247  127   0   0   0   0  \n",
       "6   195   64   0   0   0   0  \n",
       "7    39    0   0   0   0   0  \n",
       "8     0    0   0   0   0   0  \n",
       "9     0    0   0   0   0   0  \n",
       "10    0    0   0   0   0   0  \n",
       "11    0    0   0   0   0   0  \n",
       "12    0    0   0   0   0   0  \n",
       "13    0    0   0   0   0   0  \n",
       "14    0    0   0   0   0   0  \n",
       "15    0    0   0   0   0   0  \n",
       "16    0    0   0   0   0   0  \n",
       "17    0    0   0   0   0   0  \n",
       "18    0    0   0   0   0   0  \n",
       "19    0    0   0   0   0   0  \n",
       "20    0    0   0   0   0   0  \n",
       "21    0    0   0   0   0   0  \n",
       "22    0    0   0   0   0   0  \n",
       "23    0    0   0   0   0   0  \n",
       "24    0    0   0   0   0   0  \n",
       "25    0    0   0   0   0   0  \n",
       "26    0    0   0   0   0   0  \n",
       "27    0    0   0   0   0   0  \n",
       "\n",
       "[28 rows x 28 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display as text\n",
    "from IPython.display import display\n",
    "import pandas as pd\n",
    "\n",
    "print(\"Shape for dataset: {}\".format(x_train.shape))\n",
    "print(\"Labels: {}\".format(y_train))\n",
    "\n",
    "# Single MNIST digit\n",
    "single = x_train[0]\n",
    "print(\"Shape for single: {}\".format(single.shape))\n",
    "\n",
    "display(pd.DataFrame(single.reshape(28,28)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 31360,
     "status": "ok",
     "timestamp": 1558731579071,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "zhbEMQY8mp8s",
    "outputId": "663d68dd-dbb7-4166-91b6-b0737a2c117d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image (#105): Which is digit '1'\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display as image\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "digit = 105 # Change to choose new digit\n",
    "a = x_train[digit]\n",
    "plt.imshow(a, cmap='gray', interpolation='nearest')\n",
    "print(\"Image (#{}): Which is digit '{}'\".format(digit,y_train[digit]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 458
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 31360,
     "status": "ok",
     "timestamp": 1558731579072,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "cY4T9mcCmp8u",
    "outputId": "f39b4dcf-2d0c-4580-e114-9d78ac733113"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 36 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "ROWS = 6\n",
    "random_indices = random.sample(range(x_train.shape[0]), ROWS*ROWS)\n",
    "\n",
    "sample_images = x_train[random_indices, :]\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "fig, axes = plt.subplots(ROWS,ROWS, \n",
    "                         figsize=(ROWS,ROWS),\n",
    "                         sharex=True, sharey=True) \n",
    "\n",
    "for i in range(ROWS*ROWS):\n",
    "    subplot_row = i//ROWS \n",
    "    subplot_col = i%ROWS\n",
    "    ax = axes[subplot_row, subplot_col]\n",
    "\n",
    "    plottable_image = np.reshape(sample_images[i,:], (28,28))\n",
    "    ax.imshow(plottable_image, cmap='gray_r')\n",
    "    \n",
    "    ax.set_xbound([0,28])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 190
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 31360,
     "status": "ok",
     "timestamp": 1558731579073,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "yH2EoJnAmp8x",
    "outputId": "19bd4690-6209-489c-ffcb-5de0fb421163"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28, 1)\n",
      "Training samples: 60000\n",
      "Test samples: 10000\n"
     ]
    }
   ],
   "source": [
    "import tensorflow.keras\n",
    "from tensorflow.keras.datasets import mnist\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense, Dropout, Flatten\n",
    "from tensorflow.keras.layers import Conv2D, MaxPooling2D\n",
    "from tensorflow.keras import backend as K\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 12\n",
    "# input image dimensions\n",
    "img_rows, img_cols = 28, 28\n",
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(\"Training samples: {}\".format(x_train.shape[0]))\n",
    "print(\"Test samples: {}\".format(x_test.shape[0]))\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = tensorflow.keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = tensorflow.keras.utils.to_categorical(y_test, num_classes)\n",
    "model = Sequential()\n",
    "model.add(Conv2D(32, kernel_size=(3, 3),\n",
    "                 activation='relu',\n",
    "                 input_shape=input_shape))\n",
    "model.add(Conv2D(64, (3, 3), activation='relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2, 2)))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(128, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(num_classes, activation='softmax'))\n",
    "model.compile(loss='categorical_crossentropy', optimizer='adam',\n",
    "              metrics=['accuracy'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pAf59S0Wmp82"
   },
   "source": [
    "### Training/Fitting CNN - DIGITS\n",
    "\n",
    "The following code will train the CNN for 20,000 steps.  This can take awhile, you might want to scale the step count back. GPU training can help.  My results:\n",
    "\n",
    "* CPU Training Time: Elapsed time: 1:50:13.10\n",
    "* GPU Training Time: Elapsed time: 0:13:43.06"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 78971,
     "status": "ok",
     "timestamp": 1558731626687,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "5I1A6UNGmp83",
    "outputId": "3077d979-eacd-4f9a-c264-7e688f394a63"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/12\n",
      " - 99s - loss: 0.2357 - acc: 0.9292 - val_loss: 0.0531 - val_acc: 0.9827\n",
      "Epoch 2/12\n",
      " - 97s - loss: 0.0851 - acc: 0.9745 - val_loss: 0.0451 - val_acc: 0.9857\n",
      "Epoch 3/12\n",
      " - 94s - loss: 0.0622 - acc: 0.9815 - val_loss: 0.0417 - val_acc: 0.9858\n",
      "Epoch 4/12\n",
      " - 94s - loss: 0.0508 - acc: 0.9845 - val_loss: 0.0315 - val_acc: 0.9892\n",
      "Epoch 5/12\n",
      " - 94s - loss: 0.0409 - acc: 0.9872 - val_loss: 0.0295 - val_acc: 0.9904\n",
      "Epoch 6/12\n",
      " - 95s - loss: 0.0363 - acc: 0.9888 - val_loss: 0.0341 - val_acc: 0.9892\n",
      "Epoch 7/12\n",
      " - 95s - loss: 0.0346 - acc: 0.9893 - val_loss: 0.0259 - val_acc: 0.9921\n",
      "Epoch 8/12\n",
      " - 94s - loss: 0.0292 - acc: 0.9909 - val_loss: 0.0319 - val_acc: 0.9901\n",
      "Epoch 9/12\n",
      " - 95s - loss: 0.0280 - acc: 0.9912 - val_loss: 0.0295 - val_acc: 0.9915\n",
      "Epoch 10/12\n",
      " - 94s - loss: 0.0250 - acc: 0.9917 - val_loss: 0.0251 - val_acc: 0.9920\n",
      "Epoch 11/12\n",
      " - 94s - loss: 0.0224 - acc: 0.9925 - val_loss: 0.0290 - val_acc: 0.9926\n",
      "Epoch 12/12\n",
      " - 94s - loss: 0.0220 - acc: 0.9930 - val_loss: 0.0277 - val_acc: 0.9924\n",
      "Test loss: 0.027655330115636433\n",
      "Test accuracy: 0.9924\n",
      "Elapsed time: 0:19:05.38\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import time\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "model.fit(x_train, y_train,\n",
    "          batch_size=batch_size,\n",
    "          epochs=epochs,\n",
    "          verbose=2,\n",
    "          validation_data=(x_test, y_test))\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss: {}'.format(score[0]))\n",
    "print('Test accuracy: {}'.format(score[1]))\n",
    "\n",
    "elapsed_time = time.time() - start_time\n",
    "print(\"Elapsed time: {}\".format(hms_string(elapsed_time)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6JN_aTuvmp86"
   },
   "source": [
    "### Evaluate Accuracy - DIGITS\n",
    "\n",
    "Note, if you are using a GPU you might get the **ResourceExhaustedError**.  This occurs because the GPU might not have enough ram to predict the entire data set at once.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 79254,
     "status": "ok",
     "timestamp": 1558731626970,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "ZmOmMaJWmp86",
    "outputId": "896088c5-d858-47c9-92e7-dfcf6d1c00d7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss: 0.027655330115636433\n",
      "Test accuracy: 0.9924\n"
     ]
    }
   ],
   "source": [
    "# Predict using either GPU or CPU, send the entire dataset.  This might not work on the GPU.\n",
    "# Set the desired TensorFlow output level for this example\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss: {}'.format(score[0]))\n",
    "print('Test accuracy: {}'.format(score[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_musbSlQmp88"
   },
   "source": [
    "GPUs are most often used for training rather than prediction.  For prediction either disable the GPU or just predict on a smaller sample.  If your GPU has enough memory, the above prediction code may work just fine.  If not, just prediction on a sample with the following code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 80177,
     "status": "ok",
     "timestamp": 1558731627894,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "_sKiLx_ump88",
    "outputId": "82730203-9f95-4f76-eea3-2eac662b7077"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.98989898989899\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "# For GPU just grab the first 100 images\n",
    "small_x = x_test[1:100]\n",
    "small_y = y_test[1:100]\n",
    "small_y2 = np.argmax(small_y,axis=1)\n",
    "pred = model.predict(small_x)\n",
    "pred = np.argmax(pred,axis=1)\n",
    "score = metrics.accuracy_score(small_y2, pred)\n",
    "print('Accuracy: {}'.format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BqWngCONmp8-"
   },
   "source": [
    "### MNIST Fashion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 80923,
     "status": "ok",
     "timestamp": 1558731628641,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "VFjYWvJimp8_",
    "outputId": "54b12bbd-6546-4922-b0ed-a187d338ae82"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of x_train: (60000, 28, 28)\n",
      "Shape of y_train: (60000,)\n",
      "\n",
      "Shape of x_test: (10000, 28, 28)\n",
      "Shape of y_test: (10000,)\n"
     ]
    }
   ],
   "source": [
    "import tensorflow.keras\n",
    "from tensorflow.keras.callbacks import EarlyStopping\n",
    "from tensorflow.keras.layers import Dense, Dropout\n",
    "from tensorflow.keras import regularizers\n",
    "from tensorflow.keras.datasets import fashion_mnist\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = fashion_mnist.load_data()\n",
    "print(\"Shape of x_train: {}\".format(x_train.shape))\n",
    "print(\"Shape of y_train: {}\".format(y_train.shape))\n",
    "print()\n",
    "print(\"Shape of x_test: {}\".format(x_test.shape))\n",
    "print(\"Shape of y_test: {}\".format(y_test.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TRXv8k0Ymp9B"
   },
   "source": [
    "### Display the Apparel \n",
    "\n",
    "The following code shows what the Fashion MNIST files contain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 80924,
     "status": "ok",
     "timestamp": 1558731628642,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "aQbIIbpAmp9C",
    "outputId": "ccad3677-d7e4-46fb-e1d2-36156d4e7120"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape for dataset: (60000, 28, 28)\n",
      "Labels: [9 0 0 ... 3 0 5]\n",
      "Shape for single: (28, 28)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>18</th>\n",
       "      <th>19</th>\n",
       "      <th>20</th>\n",
       "      <th>21</th>\n",
       "      <th>22</th>\n",
       "      <th>23</th>\n",
       "      <th>24</th>\n",
       "      <th>25</th>\n",
       "      <th>26</th>\n",
       "      <th>27</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>144</td>\n",
       "      <td>123</td>\n",
       "      <td>23</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>107</td>\n",
       "      <td>156</td>\n",
       "      <td>161</td>\n",
       "      <td>109</td>\n",
       "      <td>64</td>\n",
       "      <td>23</td>\n",
       "      <td>77</td>\n",
       "      <td>130</td>\n",
       "      <td>72</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>216</td>\n",
       "      <td>163</td>\n",
       "      <td>127</td>\n",
       "      <td>121</td>\n",
       "      <td>122</td>\n",
       "      <td>146</td>\n",
       "      <td>141</td>\n",
       "      <td>88</td>\n",
       "      <td>172</td>\n",
       "      <td>66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>223</td>\n",
       "      <td>223</td>\n",
       "      <td>215</td>\n",
       "      <td>213</td>\n",
       "      <td>164</td>\n",
       "      <td>127</td>\n",
       "      <td>123</td>\n",
       "      <td>196</td>\n",
       "      <td>229</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>235</td>\n",
       "      <td>227</td>\n",
       "      <td>224</td>\n",
       "      <td>222</td>\n",
       "      <td>224</td>\n",
       "      <td>221</td>\n",
       "      <td>223</td>\n",
       "      <td>245</td>\n",
       "      <td>173</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>180</td>\n",
       "      <td>212</td>\n",
       "      <td>210</td>\n",
       "      <td>211</td>\n",
       "      <td>213</td>\n",
       "      <td>223</td>\n",
       "      <td>220</td>\n",
       "      <td>243</td>\n",
       "      <td>202</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>169</td>\n",
       "      <td>227</td>\n",
       "      <td>208</td>\n",
       "      <td>218</td>\n",
       "      <td>224</td>\n",
       "      <td>212</td>\n",
       "      <td>226</td>\n",
       "      <td>197</td>\n",
       "      <td>209</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>198</td>\n",
       "      <td>221</td>\n",
       "      <td>215</td>\n",
       "      <td>213</td>\n",
       "      <td>222</td>\n",
       "      <td>220</td>\n",
       "      <td>245</td>\n",
       "      <td>119</td>\n",
       "      <td>167</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>232</td>\n",
       "      <td>213</td>\n",
       "      <td>218</td>\n",
       "      <td>223</td>\n",
       "      <td>234</td>\n",
       "      <td>217</td>\n",
       "      <td>217</td>\n",
       "      <td>209</td>\n",
       "      <td>92</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>222</td>\n",
       "      <td>221</td>\n",
       "      <td>216</td>\n",
       "      <td>223</td>\n",
       "      <td>229</td>\n",
       "      <td>215</td>\n",
       "      <td>218</td>\n",
       "      <td>255</td>\n",
       "      <td>77</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>62</td>\n",
       "      <td>...</td>\n",
       "      <td>211</td>\n",
       "      <td>218</td>\n",
       "      <td>224</td>\n",
       "      <td>223</td>\n",
       "      <td>219</td>\n",
       "      <td>215</td>\n",
       "      <td>224</td>\n",
       "      <td>244</td>\n",
       "      <td>159</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "      <td>44</td>\n",
       "      <td>82</td>\n",
       "      <td>107</td>\n",
       "      <td>189</td>\n",
       "      <td>228</td>\n",
       "      <td>...</td>\n",
       "      <td>224</td>\n",
       "      <td>234</td>\n",
       "      <td>176</td>\n",
       "      <td>188</td>\n",
       "      <td>250</td>\n",
       "      <td>248</td>\n",
       "      <td>233</td>\n",
       "      <td>238</td>\n",
       "      <td>215</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>187</td>\n",
       "      <td>208</td>\n",
       "      <td>224</td>\n",
       "      <td>221</td>\n",
       "      <td>224</td>\n",
       "      <td>208</td>\n",
       "      <td>204</td>\n",
       "      <td>214</td>\n",
       "      <td>...</td>\n",
       "      <td>255</td>\n",
       "      <td>255</td>\n",
       "      <td>221</td>\n",
       "      <td>234</td>\n",
       "      <td>221</td>\n",
       "      <td>211</td>\n",
       "      <td>220</td>\n",
       "      <td>232</td>\n",
       "      <td>246</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3</td>\n",
       "      <td>202</td>\n",
       "      <td>228</td>\n",
       "      <td>224</td>\n",
       "      <td>221</td>\n",
       "      <td>211</td>\n",
       "      <td>211</td>\n",
       "      <td>214</td>\n",
       "      <td>205</td>\n",
       "      <td>205</td>\n",
       "      <td>...</td>\n",
       "      <td>188</td>\n",
       "      <td>154</td>\n",
       "      <td>191</td>\n",
       "      <td>210</td>\n",
       "      <td>204</td>\n",
       "      <td>209</td>\n",
       "      <td>222</td>\n",
       "      <td>228</td>\n",
       "      <td>225</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>98</td>\n",
       "      <td>233</td>\n",
       "      <td>198</td>\n",
       "      <td>210</td>\n",
       "      <td>222</td>\n",
       "      <td>229</td>\n",
       "      <td>229</td>\n",
       "      <td>234</td>\n",
       "      <td>249</td>\n",
       "      <td>220</td>\n",
       "      <td>...</td>\n",
       "      <td>168</td>\n",
       "      <td>219</td>\n",
       "      <td>221</td>\n",
       "      <td>215</td>\n",
       "      <td>217</td>\n",
       "      <td>223</td>\n",
       "      <td>223</td>\n",
       "      <td>224</td>\n",
       "      <td>229</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>75</td>\n",
       "      <td>204</td>\n",
       "      <td>212</td>\n",
       "      <td>204</td>\n",
       "      <td>193</td>\n",
       "      <td>205</td>\n",
       "      <td>211</td>\n",
       "      <td>225</td>\n",
       "      <td>216</td>\n",
       "      <td>185</td>\n",
       "      <td>...</td>\n",
       "      <td>239</td>\n",
       "      <td>223</td>\n",
       "      <td>218</td>\n",
       "      <td>212</td>\n",
       "      <td>209</td>\n",
       "      <td>222</td>\n",
       "      <td>220</td>\n",
       "      <td>221</td>\n",
       "      <td>230</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>48</td>\n",
       "      <td>203</td>\n",
       "      <td>183</td>\n",
       "      <td>194</td>\n",
       "      <td>213</td>\n",
       "      <td>197</td>\n",
       "      <td>185</td>\n",
       "      <td>190</td>\n",
       "      <td>194</td>\n",
       "      <td>192</td>\n",
       "      <td>...</td>\n",
       "      <td>199</td>\n",
       "      <td>206</td>\n",
       "      <td>186</td>\n",
       "      <td>181</td>\n",
       "      <td>177</td>\n",
       "      <td>172</td>\n",
       "      <td>181</td>\n",
       "      <td>205</td>\n",
       "      <td>206</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>122</td>\n",
       "      <td>219</td>\n",
       "      <td>193</td>\n",
       "      <td>179</td>\n",
       "      <td>171</td>\n",
       "      <td>183</td>\n",
       "      <td>196</td>\n",
       "      <td>204</td>\n",
       "      <td>210</td>\n",
       "      <td>...</td>\n",
       "      <td>195</td>\n",
       "      <td>191</td>\n",
       "      <td>198</td>\n",
       "      <td>192</td>\n",
       "      <td>176</td>\n",
       "      <td>156</td>\n",
       "      <td>167</td>\n",
       "      <td>177</td>\n",
       "      <td>210</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>74</td>\n",
       "      <td>189</td>\n",
       "      <td>212</td>\n",
       "      <td>191</td>\n",
       "      <td>175</td>\n",
       "      <td>172</td>\n",
       "      <td>175</td>\n",
       "      <td>181</td>\n",
       "      <td>...</td>\n",
       "      <td>210</td>\n",
       "      <td>210</td>\n",
       "      <td>211</td>\n",
       "      <td>188</td>\n",
       "      <td>188</td>\n",
       "      <td>194</td>\n",
       "      <td>192</td>\n",
       "      <td>216</td>\n",
       "      <td>170</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>66</td>\n",
       "      <td>200</td>\n",
       "      <td>222</td>\n",
       "      <td>237</td>\n",
       "      <td>239</td>\n",
       "      <td>242</td>\n",
       "      <td>...</td>\n",
       "      <td>182</td>\n",
       "      <td>182</td>\n",
       "      <td>181</td>\n",
       "      <td>176</td>\n",
       "      <td>166</td>\n",
       "      <td>168</td>\n",
       "      <td>99</td>\n",
       "      <td>58</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>61</td>\n",
       "      <td>44</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>28 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0    1    2    3    4    5    6    7    8    9   ...   18   19   20   21  \\\n",
       "0    0    0    0    0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "1    0    0    0    0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "2    0    0    0    0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "3    0    0    0    0    0    0    0    0    0    0  ...    0    1    4    0   \n",
       "4    0    0    0    0    0    0    0    0    0    0  ...   54    0    0    0   \n",
       "5    0    0    0    0    0    0    0    0    0    0  ...  144  123   23    0   \n",
       "6    0    0    0    0    0    0    0    0    0    0  ...  107  156  161  109   \n",
       "7    0    0    0    0    0    0    0    0    0    0  ...  216  163  127  121   \n",
       "8    0    0    0    0    0    0    0    0    0    1  ...  223  223  215  213   \n",
       "9    0    0    0    0    0    0    0    0    0    0  ...  235  227  224  222   \n",
       "10   0    0    0    0    0    0    0    0    0    0  ...  180  212  210  211   \n",
       "11   0    0    0    0    0    0    0    0    0    1  ...  169  227  208  218   \n",
       "12   0    0    0    0    0    0    0    0    0    0  ...  198  221  215  213   \n",
       "13   0    0    0    0    0    0    0    0    0    4  ...  232  213  218  223   \n",
       "14   0    0    1    4    6    7    2    0    0    0  ...  222  221  216  223   \n",
       "15   0    3    0    0    0    0    0    0    0   62  ...  211  218  224  223   \n",
       "16   0    0    0    0   18   44   82  107  189  228  ...  224  234  176  188   \n",
       "17   0   57  187  208  224  221  224  208  204  214  ...  255  255  221  234   \n",
       "18   3  202  228  224  221  211  211  214  205  205  ...  188  154  191  210   \n",
       "19  98  233  198  210  222  229  229  234  249  220  ...  168  219  221  215   \n",
       "20  75  204  212  204  193  205  211  225  216  185  ...  239  223  218  212   \n",
       "21  48  203  183  194  213  197  185  190  194  192  ...  199  206  186  181   \n",
       "22   0  122  219  193  179  171  183  196  204  210  ...  195  191  198  192   \n",
       "23   0    0   74  189  212  191  175  172  175  181  ...  210  210  211  188   \n",
       "24   2    0    0    0   66  200  222  237  239  242  ...  182  182  181  176   \n",
       "25   0    0    0    0    0    0    0   40   61   44  ...    0    0    0    0   \n",
       "26   0    0    0    0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "27   0    0    0    0    0    0    0    0    0    0  ...    0    0    0    0   \n",
       "\n",
       "     22   23   24   25   26   27  \n",
       "0     0    0    0    0    0    0  \n",
       "1     0    0    0    0    0    0  \n",
       "2     0    0    0    0    0    0  \n",
       "3     0    0    0    1    1    0  \n",
       "4     1    3    4    0    0    3  \n",
       "5     0    0    0   12   10    0  \n",
       "6    64   23   77  130   72   15  \n",
       "7   122  146  141   88  172   66  \n",
       "8   164  127  123  196  229    0  \n",
       "9   224  221  223  245  173    0  \n",
       "10  213  223  220  243  202    0  \n",
       "11  224  212  226  197  209   52  \n",
       "12  222  220  245  119  167   56  \n",
       "13  234  217  217  209   92    0  \n",
       "14  229  215  218  255   77    0  \n",
       "15  219  215  224  244  159    0  \n",
       "16  250  248  233  238  215    0  \n",
       "17  221  211  220  232  246    0  \n",
       "18  204  209  222  228  225    0  \n",
       "19  217  223  223  224  229   29  \n",
       "20  209  222  220  221  230   67  \n",
       "21  177  172  181  205  206  115  \n",
       "22  176  156  167  177  210   92  \n",
       "23  188  194  192  216  170    0  \n",
       "24  166  168   99   58    0    0  \n",
       "25    0    0    0    0    0    0  \n",
       "26    0    0    0    0    0    0  \n",
       "27    0    0    0    0    0    0  \n",
       "\n",
       "[28 rows x 28 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display as text\n",
    "from IPython.display import display\n",
    "import pandas as pd\n",
    "\n",
    "print(\"Shape for dataset: {}\".format(x_train.shape))\n",
    "print(\"Labels: {}\".format(y_train))\n",
    "\n",
    "# Single MNIST digit\n",
    "single = x_train[0]\n",
    "print(\"Shape for single: {}\".format(single.shape))\n",
    "\n",
    "display(pd.DataFrame(single.reshape(28,28)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 80924,
     "status": "ok",
     "timestamp": 1558731628643,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "xZOOenULmp9F",
    "outputId": "0dd20992-b596-4481-caae-8059cba0c0d7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image (#90): Which is digit '9'\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display as image\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "digit = 90 # Change to choose new article\n",
    "a = x_train[digit]\n",
    "plt.imshow(a, cmap='gray', interpolation='nearest')\n",
    "print(\"Image (#{}): Which is digit '{}'\".format(digit,y_train[digit]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 84298,
     "status": "ok",
     "timestamp": 1558731632019,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "5cN97uYTmp9H",
    "outputId": "bc794d45-c687-40b5-c7fd-29f425ffdacf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 36 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "ROWS = 6\n",
    "random_indices = random.sample(range(x_train.shape[0]), ROWS*ROWS)\n",
    "\n",
    "sample_images = x_train[random_indices, :]\n",
    "\n",
    "plt.clf()\n",
    "\n",
    "fig, axes = plt.subplots(ROWS,ROWS, \n",
    "                         figsize=(ROWS,ROWS),\n",
    "                         sharex=True, sharey=True) \n",
    "\n",
    "for i in range(ROWS*ROWS):\n",
    "    subplot_row = i//ROWS \n",
    "    subplot_col = i%ROWS\n",
    "    ax = axes[subplot_row, subplot_col]\n",
    "\n",
    "    plottable_image = np.reshape(sample_images[i,:], (28,28))\n",
    "    ax.imshow(plottable_image, cmap='gray_r')\n",
    "    \n",
    "    ax.set_xbound([0,28])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ptDi0ZiQmp9J"
   },
   "source": [
    "### Training/Fitting CNN - Fashion\n",
    "\n",
    "The following code will train the CNN for 20,000 steps.  This can take awhile, you might want to scale the step count back. GPU training can help.  My results:\n",
    "\n",
    "* CPU Training Time: Elapsed time: 1:50:13.10\n",
    "* GPU Training Time: Elapsed time: 0:13:43.06"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 84581,
     "status": "ok",
     "timestamp": 1558731632302,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "vj921rlLmp9K",
    "outputId": "db7343a0-707b-4b3f-e7a0-301a765ade1f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28, 1)\n",
      "Training samples: 60000\n",
      "Test samples: 10000\n"
     ]
    }
   ],
   "source": [
    "import tensorflow.keras\n",
    "from tensorflow.keras.datasets import mnist\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense, Dropout, Flatten\n",
    "from tensorflow.keras.layers import Conv2D, MaxPooling2D\n",
    "from tensorflow.keras import backend as K\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 12\n",
    "# input image dimensions\n",
    "img_rows, img_cols = 28, 28\n",
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(\"Training samples: {}\".format(x_train.shape[0]))\n",
    "print(\"Test samples: {}\".format(x_test.shape[0]))\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = tensorflow.keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = tensorflow.keras.utils.to_categorical(y_test, num_classes)\n",
    "model = Sequential()\n",
    "model.add(Conv2D(32, kernel_size=(3, 3),\n",
    "                 activation='relu',\n",
    "                 input_shape=input_shape))\n",
    "model.add(Conv2D(64, (3, 3), activation='relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2, 2)))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(128, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(num_classes, activation='softmax'))\n",
    "model.compile(loss='categorical_crossentropy', optimizer='adam',\n",
    "              metrics=['accuracy'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 134608,
     "status": "ok",
     "timestamp": 1558731682330,
     "user": {
      "displayName": "",
      "photoUrl": "",
      "userId": ""
     },
     "user_tz": 300
    },
    "id": "QBwmyM6hmp9L",
    "outputId": "2bb55ab4-5623-4e0b-9db5-9a3a5dacc5ba"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/12\n",
      " - 98s - loss: 0.5258 - acc: 0.8133 - val_loss: 0.3497 - val_acc: 0.8727\n",
      "Epoch 2/12\n",
      " - 94s - loss: 0.3461 - acc: 0.8759 - val_loss: 0.2829 - val_acc: 0.8954\n",
      "Epoch 3/12\n",
      " - 95s - loss: 0.2955 - acc: 0.8934 - val_loss: 0.2749 - val_acc: 0.8963\n",
      "Epoch 4/12\n",
      " - 95s - loss: 0.2655 - acc: 0.9037 - val_loss: 0.2450 - val_acc: 0.9105\n",
      "Epoch 5/12\n",
      " - 95s - loss: 0.2401 - acc: 0.9123 - val_loss: 0.2330 - val_acc: 0.9166\n",
      "Epoch 6/12\n",
      " - 94s - loss: 0.2221 - acc: 0.9173 - val_loss: 0.2235 - val_acc: 0.9196\n",
      "Epoch 7/12\n",
      " - 95s - loss: 0.2058 - acc: 0.9243 - val_loss: 0.2140 - val_acc: 0.9231\n",
      "Epoch 8/12\n",
      " - 95s - loss: 0.1905 - acc: 0.9293 - val_loss: 0.2211 - val_acc: 0.9211\n",
      "Epoch 9/12\n",
      " - 93s - loss: 0.1786 - acc: 0.9344 - val_loss: 0.2192 - val_acc: 0.9261\n",
      "Epoch 10/12\n",
      " - 95s - loss: 0.1668 - acc: 0.9388 - val_loss: 0.2149 - val_acc: 0.9269\n",
      "Epoch 11/12\n",
      " - 94s - loss: 0.1547 - acc: 0.9418 - val_loss: 0.2233 - val_acc: 0.9279\n",
      "Epoch 12/12\n",
      " - 94s - loss: 0.1438 - acc: 0.9460 - val_loss: 0.2235 - val_acc: 0.9281\n",
      "Test loss: 0.22345815933719276\n",
      "Test accuracy: 0.9281\n",
      "Elapsed time: 0:19:01.31\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import time\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "model.fit(x_train, y_train,\n",
    "          batch_size=batch_size,\n",
    "          epochs=epochs,\n",
    "          verbose=2,\n",
    "          validation_data=(x_test, y_test))\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss: {}'.format(score[0]))\n",
    "print('Test accuracy: {}'.format(score[1]))\n",
    "\n",
    "elapsed_time = time.time() - start_time\n",
    "print(\"Elapsed time: {}\".format(hms_string(elapsed_time)))"
   ]
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [
    "4aQApI1jmp8o",
    "pAf59S0Wmp82",
    "6JN_aTuvmp86",
    "BqWngCONmp8-",
    "TRXv8k0Ymp9B",
    "ptDi0ZiQmp9J",
    "FDk1ekrxmp9X",
    "SzNJPXncmp9a"
   ],
   "name": "Copy of Copy of t81_558_class06_backpropagation.ipynb",
   "provenance": [
    {
     "file_id": "https://github.com/jeffheaton/t81_558_deep_learning/blob/master/t81_558_class06_cnn.ipynb",
     "timestamp": 1558743458994
    },
    {
     "file_id": "https://github.com/jeffheaton/t81_558_deep_learning/blob/master/t81_558_class06_backpropagation.ipynb",
     "timestamp": 1558698961697
    }
   ],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3.6 (yolo)",
   "language": "python",
   "name": "yolo"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}